In his book, Christ on Earth: The Gospel Narratives as History, Dr. Jakob Van Bruggen has provided an excellent biblical and historical explanation of the night in which Jesus instituted his Supper.1 His conclusion is that on the night in which the Lord instituted his Supper, the Jews removed all leavened bread from their homes and served the first evening meal of the lamb, and that was the night of Maundy Thursday.
Because the entire argument within his book is quite extensive, and the subject so controversial, I will only quote a brief portion of his thoughts, trusting that others are already aware of the alleged "chronology contradiction" or "problem" within all four gospels. Van Bruggen writes:
After the Wednesday of the final discourses comes the first day of the Feast of Unleavened Bread (Matt. 26:17). This is when the Passover lamb is sacrificed (Mark 14:2; Luke 22:7). The days of Unleavened Bread are counted from 15 to 21 Nisan (cf. Josephus, Antiquities 3.10.5 Sec. 249), the seven days during which the Passover offerings are sacrificed in the Temple (Num. 28:16-25). Sometimes, however, 14 Nisan is also included. This is a day of preparation during which people remove all leavened bread from their homes and serve the lamb at the evening meal. In that case there are eight days of Unleavened Bread (cf. Josephus, Antiquities 2.15.1 Sec. 317). The first three evangelists (i.e. Matthew, Mark, and Luke) clearly follow the latter approach when they write about the dawn of the Thursday on which the Passover must be slaughtered (Matt. 26:17; Mark 14:12; Luke 22:7). In other words, they consider this Thursday the fourteenth day of Nisan.
The terminology used in connection with the Passover and the feast of Unleavened Bread is complicated. The fourteenth day of Nisan is the day of preparation: all leavened bread is removed from the houses, the lambs are slaughtered, and during the evening the Passover meal is eaten. Because of this evening meal, 14 Nisan is sometimes called the Passover Feast (Lev. 23:5; Josephus, Jewish War 6.9.3 Sec. 423; Antiquities 2.14.6 Sec. 313).
The fifteenth of Nisan is the beginning of the Feast of Unleavened Bread. This feast lasts seven days, during which large sacrifices are brought into the temple (Lev. 23:6; Num. 28:17-25; cf. Josephus, Antiquities 3.10.5 Sec. 249; 9.13.3 Sec. 271; 11.4.8 Sec. 110). The fifteenth day of Nisan is then counted as the first day (16 Nisan is the second day, see Josephus, Antiquities 3.10.5 Sec. 250). The fifteenth of Nisan is actually the day of Israel's liberation (Josephus, Antiquities 2.15.2 Sec. 318). The Jews also refer to the feast of Unleavened Bread (15-21 Nisan) as Passover (cf. Luke 22:1; Josephus, Jewish War 2.1.3 Sec. 10; Antiquities 10.4.5 Sec. 70; 14.2.1 Sec. 21; 17.9.3 Sec. 213; 18.2.2 Sec. 29; 20.5.3 Sec. 106).
Because the leavened bread is removed on 14 Nisan, the day is referred to as "the Day of Unleavened Bread" (Josephus, Jewish War 5.3.1 Sec. 99). If this day (14 Nisan) is counted with the feast (15-21 Nisan), one can also speak of a "period of unleavened bread" for eight days (Josephus, Antiquities 2.15.1 Sec. 317; cf. Mark 14:12; Luke 22:1).2
1. Jakob Van Bruggen, Christ on Earth: The Gospel Narratives as History [Grand Rapids, MI: Baker Books; 1998] pp. 212-219
2. Ibid. p. 212-213.